Subgroups — #14909394

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079252	C₂	1	2	yes	maximal, complemented
2	#13070898	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070852	C₂	1	2	yes	maximal, complemented
4	#13070721	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070716	C₂	1	1	yes	maximal, characteristic
6	#13070709	C₂	1	2	yes	maximal, complemented
7	#13070492	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070487	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₃₂×Dic₁₁	C₂	1	2	yes	maximal, complemented
10	#13070211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2249	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623213	—	2	2	no	—
13	C₂×C₁₁×Q₃₂	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₁₁×D₁₆	C₂²	1	1	yes	characteristic
16	C₁₁×#495	C₂²	1	2	yes	—
17	#10622801	C₂²	1	2	yes	—
18	Q₁₆×Dic₁₁	C₂²	1	2	yes	—
19	#10622787	—	2	2	no	—
20	#10622777	—	2	2	no	—
21	#10622770	C₂²	1	2	yes	—
22	D₈×Dic₁₁	C₂²	1	2	yes	—
23	#10622668	—	2	2	no	—
24	C₂×#66862	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
26	#10622302	C₂²	1	1	yes	characteristic
27	#10622295	C₂²	1	2	yes	—
28	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
29	#10622202	C₂²	1	2	yes	—
30	#10622202	C₂²	1	2	yes	—
31	#10622200	C₂²	1	2	yes	—
32	#10622200	C₂²	1	2	yes	—
33	#10622143	C₂²	1	2	yes	—
34	#10622143	C₂²	1	1	yes	characteristic
35	#10622143	C₂²	1	1	yes	characteristic
36	#10622140	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
38	#10622099	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₂×C₁₁×SD₁₆	—	2	2	no	—
41	C₂×C₁₁×D₈	C₂³	1	2	yes	—
42	C₁₁×#124	—	2	2	no	—
43	#66999	—	2	2	no	—
44	Q₈×Dic₁₁	—	2	2	no	—
45	#66991	—	2	2	no	—
46	D₄×Dic₁₁	—	2	2	no	—
47	C₂×#4313	D₄	1	1	yes	characteristic
48	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
49	#66939	—	4	2	no	—
50	#66938	—	4	2	no	—
51	#66932	—	4	2	no	—
52	#66931	—	4	2	no	—
53	#66925	D₄	1	1	yes	characteristic
54	#66922	—	2	2	no	—
55	C₁₁×Q₃₂	—	2	2	no	—
56	C₁₁×SD₃₂	—	2	4	no	—
57	C₁₁×D₁₆	—	2	2	no	—
58	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	#66899	—	2	2	no	—
62	#66899	—	2	2	no	—
63	#66896	—	2	2	no	—
64	#66896	—	2	2	no	—
65	#66882	—	2	2	no	—
66	#66882	C₂³	1	2	yes	—
67	#66882	C₂³	1	2	yes	—
68	#66879	D₄	1	1	yes	characteristic
69	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
70	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
72	#66867	D₄	1	1	yes	characteristic
73	#66862	—	2	2	no	—
74	C₁₆×D₁₁	—	2	2	no	—
75	#33742	—	11	1	no	maximal, Sylow
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×D₄×C₁₁	—	2	2	no	—
78	C₂×C₂²⋊D₁₁	—	4	2	no	—
79	C₂²×Dic₁₁	—	4	2	no	—
80	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂×Dic₂₂	—	4	2	no	—
82	C₁₁×Q₁₆	—	2	2	no	—
83	C₁₁×Q₁₆	—	2	2	no	—
84	C₁₁×SD₁₆	—	4	4	no	—
85	C₁₁×D₈	—	2	2	no	—
86	C₁₁×D₈	—	2	2	no	—
87	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
89	C₁₁×C₂²⋊C₄	—	4	2	no	—
90	C₁₁×C₂²⋊C₄	—	4	2	no	—
91	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂²⋊Dic₁₁	—	4	2	no	—
93	C₂²⋊Dic₁₁	—	4	2	no	—
94	(C₂×D₁₁)⋊C₄	—	4	2	no	—
95	(C₂×D₁₁)⋊C₄	D₈	1	2	yes	—
96	C₄⋊Dic₁₁	—	2	2	no	—
97	C₄⋊Dic₁₁	—	2	2	no	—
98	C₄⋊Dic₁₁	—	4	2	no	—
99	C₄⋊Dic₁₁	—	4	2	no	—
100	Dic₁₁⋊C₄	—	4	2	no	—
101	Dic₁₁⋊C₄	D₈	1	2	yes	—
102	C₄×Dic₁₁	—	4	2	no	—
103	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
106	#4313	—	2	2	no	—
107	C₈×D₁₁	—	2	1	no	—
108	C₈×D₁₁	—	2	1	no	—
109	C₁₁×C₁₆	#41	1	2	yes	—
110	C₁₁×C₁₆	#41	1	2	yes	—
111	C₁₁⋊C₁₆	—	2	1	no	—
112	C₁₁⋊C₁₆	—	2	1	no	—
113	#3175	—	11	2	no	—
114	#2254	—	11	1	no	—
115	#2249	D₁₁	1	1	yes	characteristic, complemented
116	#2243	—	11	2	no	—
117	#2219	—	11	1	no	—
118	#2218	—	11	1	no	—
119	#2217	—	11	2	no	—
120	#2177	—	11	1	no	—
121	#2176	—	11	1	no	—
122	C₄×SD₃₂	—	11	2	no	—
123	#2108	—	11	1	no	—
124	C₂³×C₁₁	—	4	2	no	—
125	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
126	Q₈×C₁₁	—	4	2	no	—
127	Q₈×C₁₁	—	4	2	no	—
128	D₄×C₁₁	—	4	2	no	—
129	D₄×C₁₁	—	4	2	no	—
130	C₂×C₄×C₁₁	—	4	2	no	—
131	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
132	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
133	C₂²⋊D₁₁	—	16	2	no	—
134	C₂×Dic₁₁	—	4	2	no	—
135	C₂×Dic₁₁	—	4	2	no	—
136	C₂×Dic₁₁	—	16	2	no	—
137	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
138	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
139	C₄×D₁₁	—	2	1	no	—
140	C₄×D₁₁	—	2	1	no	—
141	Dic₂₂	—	16	2	no	—
142	C₈×C₁₁	#135	1	2	yes	—
143	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
144	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
145	C₁₁⋊C₈	—	2	1	no	—
146	C₁₁⋊C₈	—	2	1	no	—
147	#542	—	22	2	no	—
148	C₂×Q₃₂	C₂×D₁₁	1	1	yes	characteristic
149	C₂×SD₃₂	C₂×D₁₁	1	2	yes	—
150	C₂×D₁₆	C₂×D₁₁	1	1	yes	characteristic
151	C₂×M₃₂	—	11	1	no	—
152	C₂²×C₁₆	—	11	1	no	—
153	#500	—	11	2	no	—
154	#495	C₂×D₁₁	1	2	yes	—
155	#489	—	22	2	no	—
156	#468	—	22	2	no	—
157	#467	—	11	2	no	—
158	#466	—	11	2	no	—
159	#440	—	22	2	no	—
160	C₄×Q₁₆	—	11	2	no	—
161	C₄×D₈	—	11	2	no	—
162	#405	—	11	1	no	—
163	#367	—	11	2	no	—
164	#367	—	11	1	no	—
165	#367	—	11	1	no	—
166	#358	—	11	2	no	—
167	#358	—	11	2	no	—
168	#357	—	11	2	no	—
169	#357	—	11	2	no	—
170	#346	—	11	1	no	—
171	#346	—	11	1	no	—
172	C₄×C₁₆	—	11	1	no	—
173	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
174	C₂²×C₁₁	—	8	2	no	—
175	C₂²×C₁₁	—	8	2	no	—
176	C₂²×C₁₁	—	8	2	no	—
177	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
178	C₂×D₁₁	—	2	2	no	—
179	C₂×D₁₁	—	2	1	no	—
180	C₄×C₁₁	—	2	2	no	—
181	C₄×C₁₁	—	8	2	no	—
182	C₄×C₁₁	#532	1	1	yes	characteristic
183	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
184	Dic₁₁	—	2	2	no	—
185	Dic₁₁	—	2	1	no	—
186	Dic₁₁	—	8	2	no	—
187	Dic₁₁	—	8	2	no	—
188	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
189	C₂×SD₁₆	—	2	2	no	—
190	C₂×D₈	C₂²×D₁₁	1	2	yes	—
191	C₂×M₁₆	—	11	1	no	—
192	C₂²×C₈	—	11	1	no	—
193	C₄⋊Q₈	—	22	2	no	—
194	#126	—	44	2	no	—
195	#124	—	2	2	no	—
196	#124	—	44	2	no	—
197	#123	—	44	2	no	—
198	C₂²⋊Q₈	—	22	2	no	—
199	C₂²⋊Q₈	—	44	2	no	—
200	#121	—	22	2	no	—
201	C₄×Q₈	—	22	2	no	—
202	C₄×D₄	—	22	2	no	—
203	#117	—	11	1	no	—
204	Q₃₂	—	2	2	no	—
205	SD₃₂	—	2	4	no	—
206	D₁₆	—	2	2	no	—
207	M₃₂	—	22	2	no	—
208	C₂×C₁₆	—	11	1	no	—
209	C₂×C₁₆	—	11	1	no	—
210	C₂×C₁₆	—	22	2	no	—
211	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
212	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
213	#107	—	11	2	no	—
214	#107	—	11	2	no	—
215	#107	—	22	2	no	—
216	#103	—	22	2	no	—
217	#103	—	22	2	no	—
218	#102	—	22	2	no	—
219	#102	—	22	2	no	—
220	#97	—	11	1	no	—
221	#97	—	11	1	no	—
222	C₄×C₈	—	11	1	no	—
223	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
224	C₂×C₁₁	—	16	2	no	—
225	C₂×C₁₁	#3169	1	1	yes	characteristic
226	C₂×C₁₁	#3416	1	2	yes	—
227	D₁₁	—	4	1	no	—
228	C₂×Q₈	—	2	2	no	—
229	C₂×Q₈	—	44	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	44	2	no	—
232	C₂²×C₄	—	11	1	no	—
233	C₂²×C₄	—	44	2	no	—
234	Q₁₆	—	2	2	no	—
235	Q₁₆	—	2	2	no	—
236	SD₁₆	—	4	4	no	—
237	D₈	—	2	2	no	—
238	D₈	—	2	2	no	—
239	M₁₆	—	22	2	no	—
240	C₂×C₈	—	11	1	no	—
241	C₂×C₈	—	11	1	no	—
242	C₂×C₈	—	22	1	no	—
243	C₂×C₈	—	22	1	no	—
244	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
245	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
246	C₄⋊C₄	—	11	2	no	—
247	C₄⋊C₄	—	22	2	no	—
248	C₄⋊C₄	—	22	2	no	—
249	C₄⋊C₄	—	44	2	no	—
250	C₄⋊C₄	—	44	2	no	—
251	C₄⋊C₄	—	44	2	no	—
252	C₂²⋊C₄	—	4	2	no	—
253	C₂²⋊C₄	—	4	2	no	—
254	C₂²⋊C₄	—	11	2	no	—
255	C₂²⋊C₄	—	44	2	no	—
256	C₂²⋊C₄	—	44	2	no	—
257	C₂²⋊C₄	—	44	2	no	—
258	C₄²	—	11	1	no	—
259	C₄²	—	44	2	no	—
260	C₄²	D₄×D₁₁	1	1	yes	characteristic
261	C₁₆	—	22	1	no	—
262	C₁₆	—	22	1	no	—
263	C₁₆	#4341	1	2	yes	—
264	C₁₆	#4341	1	2	yes	—
265	C₁₁	#33742	1	1	yes	characteristic, complemented, Sylow
266	C₂³	—	4	2	no	—
267	C₂³	—	11	1	no	—
268	Q₈	—	4	2	no	—
269	Q₈	—	4	2	no	—
270	Q₈	—	176	2	no	—
271	D₄	—	4	2	no	—
272	D₄	—	4	2	no	—
273	D₄	—	176	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	11	2	no	—
276	C₂×C₄	—	11	1	no	—
277	C₂×C₄	—	22	1	no	—
278	C₂×C₄	—	22	1	no	—
279	C₂×C₄	—	44	2	no	—
280	C₂×C₄	—	44	2	no	—
281	C₂×C₄	—	176	2	no	—
282	C₂×C₄	D₈×D₁₁	1	2	yes	—
283	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
284	C₈	—	22	1	no	—
285	C₈	—	22	1	no	—
286	C₈	#66965	1	2	yes	—
287	C₈	C₂×#4341	1	1	yes	characteristic
288	C₈	C₂×#4341	1	1	yes	characteristic
289	C₂²	—	8	2	no	—
290	C₂²	—	8	2	no	—
291	C₂²	—	8	2	no	—
292	C₂²	—	22	1	no	—
293	C₂²	—	22	2	no	—
294	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
295	C₄	—	2	2	no	—
296	C₄	—	8	2	no	—
297	C₄	—	22	1	no	—
298	C₄	—	22	2	no	—
299	C₄	—	88	2	no	—
300	C₄	—	88	2	no	—
301	C₄	#10623247	1	1	yes	characteristic
302	C₄	C₂×#66965	1	1	yes	characteristic
303	C₂	—	16	2	no	—
304	C₂	—	44	1	no	—
305	C₂	#13079193	1	1	yes	characteristic
306	C₂	#13081759	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2249	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	#13070716	C₂
hypercenter	#2249	D₁₁
hypocenter	C₁₁	#33742
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2249

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #13079252	C₂	semidirect
2. #13070898	C₂	semidirect
3. #13070852	C₂	semidirect
4. #13070721	C₂	semidirect
6. #13070709	C₂	semidirect
7. #13070492	C₂	semidirect
8. #13070487	C₂	semidirect
9. SD₃₂×Dic₁₁	C₂	semidirect
10. #13070211	C₂	semidirect
11. C₁₁×#2249	C₂	semidirect
115. #2249	D₁₁	semidirect
265. C₁₁	#33742	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13079252	2
#13070898	2
#13070852	2
#13070721	2
#13070716	2
#13070709	2
#13070492	2
#13070487	2
SD₃₂×Dic₁₁	2
#13070211	2
C₁₁×#2249	2
#33742	11